Edit Mode Changes not showing up in Object Mode
If your active Object is an armature

When you have an Armature in Edit mode, then you always see the Bones in Rest Pose. While when you switch to Pose Mode or Object mode, then you see the object in its current pose.

You can get out of this by resetting your pose to pose mode:


enter pose mode
Select all bones ( A )
Then type: ALT RALT SALT G to reset rotations, scales and locations of your pose bones. Or alternatively from within the 3D Viewport footer navigate to: Pose -> Clear Transform -> All


If your active Object is a Rigged Mesh

Then the object is (most probably) assigned to an Armature via the modifier Stack. In that case the Object by default gets displayed in Rest Pose when you edit the mesh. In the image below you see the object aligned to the Armature Pose when in Object mode(left side), but displayed in Rest Pose when in edit mode(right side).



However, you can force to display the effect of the Modifier in edit mode as well:


Open the Modifier Stack
In the Armature modifier set the options (see image)


Display Modifier in edit Mode
Adjust edit Cage to Modifier result (see note below)





Note: The tool tip text is from upcoming Blender 2.72 In older Blender releases the text was: Apply modifier to editing cage during edit mode